HKDSE M2 Question Review (20241024)

Just a take-home mock exam.

Make good use of Internet technologies.

1. Consider mx+ny = k, where x and y are variables.

(a) What is meant by geometric mean?

(b) Hence, derive xy= constant

(c) Given 5 variables a, b, c, d and e.

(i) What are their geometric mean?

(ii) Hence, show that (i) is non-Abelian.

2. A rectangular hyperbola is know to be exhibiting inverse proportion.

(a) Explain how it is transformed from a general hypebola.

(b) Discuss how, from (a), the hyperbolas are transformed into exponential functions and logarithmic function with the line of symmetry y=x.

(c) Describe how the shortest distance between 2 hyperbolas can be computed.

3. Google the Fundamental Theorem of Algebra.

(a) Explain why in calculating alternative currents engineering questions, complex numbers are often deployed.

(b) Explain why Argand Diagrams effectively describe complex numbers even if they are not comparable.

(c) In a polynomial, why the degree can't be below zero?

4. Notice 3D vectors.

(a) Explain how the direction of a vector product is defined in both translation and rotation.

(b) What is meant by a skew line?

(c) Why do we say Pressure is a tensor?

以上題目，全部今日嘅中學唔會見到，

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亦寄予各位DSE狀元，天外有天

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5. This question is within the syllabus:

1. What is the scalar product in matrix form?

2. What is the implications of Cartesian products in your HKDSE Core/M1/M2 study?

6. Read the following texts:

Google Mean Value Theorem (MVT) , and suggest 3 more applications to MVT in HKAL Pure Mathematics (1985-2013) curriculum.

7. Discuss the use of the below rules of thumb in HKDSE probability syllabi:

1. Inclusion-Exclusion Principle

2. Piegonhole Principle

Pigeonhole*

8. Writing an essay on math is essential to training mathematical thinking. Explain why douchebags from local examination boards never practise so.

12. Why HKDSE never asks students to use Libreoffice Math or LateX for presentations?

9. Why HKDSE never asks students to use Libreoffice Math or LaTeX for presentations?

10. How to use physical instruments to locate the center of a circle?

11. What is meant by logistic growth and decay, as well as its applications to biology and economics?

12. 有港女說數學乃無聊玩意。試駁斥此說法。